Omar is 2 times as old as Luis. Eighteen years ago, Omar was 5 times as old as Luis. How old is Omar now?
Answer: We can use the given information to write down two equations that describe the ages of Omar and Luis. Let Omar's current age be $o$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $o = 2l$ Eighteen years ago, Omar was $o - 18$ years old, and Luis was $l - 18$ years old. The information in the second sentence can be expressed in the following equation: $o - 18 = 5(l - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $o$ , it might be easiest to solve our first equation for $l$ and substitute it into our second equation. Solving our first equation for $l$ , we get: $l = o / 2$ . Substituting this into our second equation, we get: $o - 18 = 5($ $(o / 2)$ $- 18)$ which combines the information about $o$ from both of our original equations. Simplifying the right side of this equation, we get: $o - 18 = \dfrac{5}{2} o - 90$ Solving for $o$ , we get: $\dfrac{3}{2} o = 72$ $o = \dfrac{2}{3} \cdot 72 = 48$.